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<h1 class="reftitle">AffFunction</h1>
<h2>Purpose</h2>
<p>Representation of affine functions in the form F*x + g</p>
<h2>Syntax</h2>
<pre class="synopsis">L = AffFunction(F,g)</pre>
<pre class="synopsis">L = AffFunction(F)</pre>
<pre class="synopsis">L = AffFunction(F,g,Data)</pre>
<h2>Description</h2>
<p></p>
        The <tt>AffFunction</tt> class represents affine functions of the form <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction1.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction1.png"> 
        where <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction2.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction2.png"> is a real matrix and <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction3.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction3.png"> is a real column vector. Dimensions of <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction4.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction4.png">
        and <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction5.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction5.png"> must coincide such that the output is a vector or scalar.               
	<h2>Input Arguments</h2>
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<td><tt>F</tt></td>
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<p></p>Real matrix representing the coefficients in the linear term <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction6.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction6.png"> in  <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction7.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction7.png">.
        <p>
	    		Class: <tt>double</tt></p>
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<td><tt>g</tt></td>
<td>
<p></p>Real vector representing the affine terms <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction8.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction8.png"> in  <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction9.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction9.png">.
        <p>
	    		Class: <tt>double</tt></p>
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<td><tt>Data</tt></td>
<td>
<p></p>Any data related to the function.
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<h2>Output Arguments</h2>
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<td><tt>L</tt></td>
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<p></p> 
         <tt>AffFunction</tt> object. </td>
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<h2>Example(s)</h2>
<h3>Example 
				1</h3>Construct affine function <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction10.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction10.png"> 
      <pre class="programlisting">L = AffFunction(3,1)</pre>
<pre class="programlisting">Affine Function: R^1 -&gt; R^1
</pre>Construct linear function <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction11.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction11.png"> 
      <pre class="programlisting">k = AffFunction(2*pi)</pre>
<pre class="programlisting">Affine Function: R^1 -&gt; R^1
</pre>
<h3>Example 
				2</h3>Construct vectorized affine function <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction12.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction12.png">
            with respect to vector <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction13.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction13.png"> with two elements<pre class="programlisting"> F = AffFunction([1 2;3 4],[1; -1]) </pre>
<pre class="programlisting">Affine Function: R^2 -&gt; R^2
</pre>
<h3>Example 
				3</h3> Construct affine function <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction14.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction14.png"> where <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction15.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction15.png"> and <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction16.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction16.png"> are regression coefficients from
        the data <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction17.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction17.png"> and <img src="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction18.png" alt="../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction18.png">.  The data we want to store <pre class="programlisting"> data.x = 0:0.01:0.5;</pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> data.y = sin(data.x);</pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> data.file= 'DSCa001';</pre>
<pre class="programlisting"></pre> Compute the regression coefficients and store them in <tt>h</tt>
      <pre class="programlisting"> h = polyfit(data.x,data.y,1); </pre>
<pre class="programlisting"></pre> We can store the data from which the function was obtained under <tt>Data</tt> property <pre class="programlisting"> A=AffFunction(h(1),h(2),data)</pre>
<pre class="programlisting">Affine Function: R^1 -&gt; R^1
</pre>
<h2>See Also</h2>
<a href="../@Function/function.html">function</a>, <a href="../@QuadFunction/quadfunction.html">quadfunction</a><p></p>
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<br><p>©  <b>2010-2013</b>     Martin Herceg: ETH Zurich,    <a href="mailto:herceg@control.ee.ethz.ch">herceg@control.ee.ethz.ch</a></p>
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